Metamaterial homogenization is often based on implicit assumptions inspired by natural material models. However, retrieved permittivity and permeability frequently retain nonphysical values, especially near the metamaterial resonances where most interesting features are expected. We explain here the nature of typical homogenization artifacts, relating them to an inherent form of magnetoelectric coupling associated with the finite phase velocity along metamaterial arrays. Our findings allow restoring the proper definition and physical meaning of local constitutive parameters for metamaterials

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